Geographically weighted regression for modelling the

Abstract

Accessibility models in transport geography based on geographicinformation systems have proven to be an effective method in deter-mining spatial inequalities associated with public health. This workaims to model the spatial accessibility from populated areas within theConcepción metropolitan area (CMA), the second largest city in Chile.The city’s public hospital network is taken into consideration with spe-cial reference to socio-regional inequalities. The use of geographicallyweighted regression (GWR) and ordinary least squares (OLS) for mod-elling accessibility with socioeconomic and transport variables is pro-posed. The explanatory variables investigated are: illiterate popula-tion, rural housing, alternative housing, homes with a motorised vehi-cle, public transport routes, and connectivity. Our results identify thatapproximately 4.1% of the population have unfavourable or veryunfavourable accessibility to public hospitals, which correspond torural areas located south of CMA. Application of a local GWR model(0.87 R2 adjusted) helped to improve the settings over the use of tradi-tional OLS methods (multiple regression) (0.67 R2 adjusted) and tofind the spatial distribution of both coefficients of the explanatory vari-

ables, demonstrating the local significance of the model. Thus, acces-sibility studies have enormous potential to contribute to the develop-ment of public health and transport policies in turn to achieve equalityin spatial accessibility to specialised health care.

Introduction

In recent years, numerous studies using tools based on geographicinformation systems (GIS) have been carried out to assess the impactof accessibility on territorial imbalances of relevant aspects such aspublic health. This information provides important opportunities toassess the spatial distribution of hospital facilities and primary healthcare (Ramírez and Bosque Sendra, 2001; Schuurman et al., 2006;Sasaki et al., 2010; Buzai, 2011). These studies have also enabled theidentification of served and/or non-served areas as well as of the ben-eficiary and/or deprived socio-spatial groups regarding accessibility(Fuenzalida, 2010).

In this context, geographical studies – developed in Latin Americaand carried out from a spatial and automated approach – generallyfocus on planning, location, and territorial management of health serv-ices. These studies have aimed to assess how the population is guar-anteed equitable access to facilities, according to coverage areas, tak-ing into account both primary and specialised care. The spatial expres-sion of the health system implies, at the same time, an equitable geo-graphical distribution of the centres providing health services to thepopulation. However, the transportation system, which in the endenables the mobility of the population, has seldom been considered.Nevertheless, these studies show variation in accessibility levels. Inthis regard, Dewulf et al. (2013) evaluated the results of different GISmethods, which have the main problem of not capturing local, spatialvariations. However, if cumulative opportunity measures are consid-ered as an accessibility indicator, it is relevant to include the travelpatterns and socio-demographic characteristics of the population(Páez et al., 2010).

In the Concepción metropolitan area (CMA), there are 228 localities(30 urban and 198 rural) distributed among different municipalitiesand census districts. Some localities possessing high population den-sity do not have hospitals or primary health care centres. Many ofthese localities are more rural than city-like and the roads are gener-ally poor, preventing proper connectivity with the urban areas wherehealth care infrastructure is located. Considering these aspects, aswell as the socio-economic characteristics and material circumstancesof the population treated in public hospitals, it is important to modelthe accessibility to these facilities in CMA in order to determine theexisting inequalities in the territory. Hence, our study represents acontribution to the search for alternatives that can solve this accessi-bility problem.

Correspondence: Carolina Rojas Quezada, Department of Geography,University of Concepción, Calle Victoria S/N, Barrio UniversitarioConcepción, Chile. Tel. +56.041.2203233 - Fax: +56.041.2207396.E-mail: [email protected]

Key words: Accessibility; Spatial equity; Hospital facility; Geographicallyweighted regression; Chile.

Acknowledgements: the following projects are thanked: FONDAP CONICYT15110020 CEDEUS; GESITRAN Innova Biobío ibb-11-PCS2-1116; FONDECYT1150239. Contributions of Ph.D. Juan Carrasco and Ph.D. Alejandro Tudela,University of Concepción, are also thanked.

Received for publication: 13 January 2016.Revision received: 23 May 2016.Accepted for publication: 24 May 2016.

©Copyright M.M. Bascuñán and C.R. Quezada, 2016Licensee PAGEPress, ItalyGeospatial Health 2016; 11:451doi:10.4081/gh.2016.451

This article is distributed under the terms of the Creative CommonsAttribution Noncommercial License (CC BY-NC 4.0) which permits any non-commercial use, distribution, and reproduction in any medium, provided theoriginal author(s) and source are credited.

Geographically weighted regression for modelling the accessibility to the public hospital network in Concepción Metropolitan Area, ChileMarcela Martínez Bascuñán,1 Carolina Rojas Quezada1,21Centre for Urban Sustainable Development, University of Concepción; 2Department ofGeography, University of Concepción, Concepción, Chile

[Geospatial Health 2016; 11:451] [page 263]

Geospatial Health 2016; volume 11:451

gh-2016_3.qxp_Hrev_master 16/11/16 15:18 Pagina 263

Non co

mmercial

use o

nly

[page 264] [Geospatial Health 2016; 11:451]

The aim of this work is to model the spatial accessibility of the pop-ulated urban and rural settlements of CMA to the public health care sys-tem considering the transportation network as the cornerstoneenabling accessibility from the localities and spatial variations. Overall,our study has the purpose of identifying and analysing social and terri-torial imbalances.

Materials and Methods

Study areaCMA is composed of 11 municipalities that house a total population

of 966,411 residents (INE, 2002). The majority of the population is con-centrated in Concepción and Talcahuano, and these cities are high-lighted as the principal urban articulators in this industrial area of themetropolitan territory. The 11 municipalities are comprised of 121 cen-tral districts and 228 localities (Figure 1). In this study, 119 census dis-tricts of CMA were considered, excluding the districts corresponding toQuiriquina (Talcahuano) and Santa María (Coronel) islands. Theexplanatory variables investigated were captured based on that territo-rial unit.

The geographic unit that subdivides the municipalities is the censusdistrict, which was chosen for this study as it incorporates characteris-tics of the population, homes, and dwellings in both urban and ruralareas with a number of spatial units appropriate for modelling at thelocal level. Furthermore, the territory in which human settlements arelocated constitutes what is called a locality in terms of the census.According to the population numbers and the type of predominant eco-nomic activity, localities are classified as urban or rural. In CMA, it ispossible to find one or more localities per district that provide levelsthat are particularly representative of travel times and therefore servethe purpose of calculating accessibility. Thus, the main point is consid-ering the location of the settlement but not centroid of the district,which in many cases does not adequately describe population distribu-tion (Figure 1).

DataWe used the road network to compute the shortest travel times from

localities to hospitals. To model the road network, the functionalities oftopology of ArcGIS (ESRI, Redlands, CA, USA) were used. The state,concession and urban highways of the municipality that are part ofCMA were included at a 1:10,000 scale, updated to the year 2013 by theMinistry of Housing and Urban Planning. The road data has basic char-acteristics such as: measure of length for each section, speed limit, andtype of road. Localities are represented by a georeferenced element(point) and the census districts as polygons, both obtained from theGIS Database of the National Statistical Institute of Chile (INE, 2002).

Before applying regression methods to model accessibility, a correla-tion analysis was performed among the set of candidate explanatoryvariables. In correspondence to Bocco et al. (2000) and Rojas et al.(2013), values with correlations larger than 0.8 were discarded in orderto avoid possible problems with multicollinearity. In this study thesevalues were found for occupation (positive correlation with homes witha vehicle), ethnicity (positive correlation with illiterate population)and housing with deficient sanitary services (positive correlation withalternative housing). The analysis of Pearson�s bivariate correlations(Bollen and Barb, 1981) is presented with the variables that showedcorrelations below 0.8 and therefore chosen for the modelling (Table1). Moran’s I (Fotheringham et al., 2002; Patel and Waters, 2012) wasapplied to the six explanatory variables in order to verify the presenceor absence of the spatial autocorrelation in its distributions. Resultsshowed that for all the variables, Moran’s I suggested a spatial autocor-relation that was statistically significant with a clustered distribution(Table 2). Thus, both the Z score and P value indicate rejection of thenull hypothesis (which establishes that the entity values are distrib-uted randomly in the studied area).

Article

Table 1. Bivariate correlations between explanatory variables.

Public transport Connectivity Homes with a Rural housing Alternative Illiterate routes vehicle housing population

Public transport routes 1 Connectivity 0.666 1 Homes with a vehicle 0.343 0.215 1 Rural housing -0.483 -0.530 -0.293 1 Alternative housing 0.215 0.160 -0.072 0.002 1 Illiterate population 0.114 0.085 -0.062 0.024 0.587 1

Figure 1. Concepción metropolitan study area with locality, cen-sus district and municipality boundaries.


Non co

mmercial

use o

nly

In order to model public health care accessibility, six potentiallyexplanatory socio-economic and transportation variables were used.Four variables were chosen from the 2002 National Population andHousing Census with reference to the hierarchies of People, Housing,and Homes (INE, 2002), while two were obtained from the GesitranBiobio project (www.gesitranbiobio.cl), related to the Transportationhierarchy (number of public transport routes and connectivity index).Table 3 presents the list of variables and their descriptions.

Extraction of the census variables was carried out with the free soft-ware developed by CEPAL, REDATAM R+SP Process (CEPAL, Santiagode Chile, Chile; Fuenzalida et al., 2014; Villanueba, 2010). This pro-gramme is capable of processing census data, and was used for the2002 data mentioned earlier. Also, information can be disaggregatedinto different geographic units.

Accessibility modelling methodNetwork Analyst, a package extension included in ArcGIS (ESRI),

was used to calculate minimal routes between localities and hospitalsin order to obtain origin-destination travel time matrices. The calcula-tion of accessibility was based on the average of impedances that sep-arate each locality from the hospital centres through the networkwhere the number of hospitals of destination had been previouslyassigned according to the municipality to which they belong.Therefore, in this research, accessibility should be understood as theaverage travel time from each locality to its assigned hospital.

The hospital network of CMA’s health system is comprised of sevenestablishments belonging to the public health services of Concepción(CPHS) and those belonging to Talcahuano (TPHS). The municipali-

Article


Table 2. Spatial autocorrelation for explanatory variables.

Variable Moran’s I Pattern Z-score* P°

Public transport routes 0.502 Clustered 12.346 0.000Connectivity 0.687 Clustered 16.728 0.000Homes with a vehicle 0.201 Clustered 5.231 0.000Rural housing 0.342 Clustered 8.631 0.000Alternative housing 0.511 Clustered 11.369 0.000Illiterate population 0.454 Clustered 6.385 0.000*Measure of standard deviation; °the probability of obtaining an observed pattern. P<0.05

Table 3. Explanatory variables selected for the regression models.

Hierarchy Variable Description Scale/level Source

People Illiterate population Percentage of people ≥5 District INE (2002) years old who cannot read or write, per census district, with respect to the total population Housing Rural housing Percentage of rural District INE (2002) housing by census district, with respect to the total number of dwellings Alternative housing Percentage of housing District INE (2002) considered as shacks, farm housing, huts or mobile units (tent or container) per census district out of the total of dwellings Home Homes with a motorised vehicle Percentage of homes that District INE (2002) have a car, van, pick-up or truck available for personal use by census district with respect to the number of total homes Transport Public transport route Number of public District Prepared by the authors transport routes (with city, based on intercity and rural buses, http://www.gesitranbiobio.cl shared taxis or passenger trains) passing through each census district Connectivity Index that relates the District http://www.gesitran biobio.cl number of network arcs with the number of network nodes per census district


Non co

mmercial

use o

nly


ties found within CPHS are Concepción, Chiguayante, Hualqui, SanPedro de la Paz, Coronel, and Lota. TPHS has centres in the cities ofTalcahuano, Hualpén, Penco, and Tomé. It is important to note that theCMA population can only be assigned to one hospital (called the mainor the primary hospital), while localities do not have this facility intheir municipality. Localities assigned to two hospitals can eitheraccess the establishment placed in their municipality of origin or theirmain hospital (Regional Hospital- Higueras Hospital) as shown inFigure 2.

Taking the localities as a unit of origin, an aggregation of values wasdone considering the average travel times from these localities to thedistrict level for their incorporation as a dependent variable in the mod-elling. The travel times were integrated into diverse studies in order tomodel accessibility to primary health care centres/hospitals (Brabynand Skelly, 2001; Hare and Barcus, 2007; Bagheri et al., 2009;Rodríguez, 2010; Munoz and Kallestal, 2012), where the location factor(population, health care centres) and the characteristics of the net-work were considered in order to obtain the travel time factor (speedand length of the road sections).

Spatial regression methodsThe accessibility was analysed as a variable dependent on ordinary

least squares (OLS) according to Gutiérrez et al. (2012), and on geo-graphically weighted regression (GWR) according to Fotheringham etal. (2002). The former is a global method based on the use of only oneequation to explore the relationship between variables. In this model,it is assumed that the relationship is consistent throughout the wholestudy area (stationary), without considering the possibility that localvariations exist due to the heterogeneity of the space. The latter is alocal regression model that creates an equation for each element of thedependent variable data set, in order to capture geographic variations.

Global regression (OLS) can be represented by the equation (1):

(eq. 1)

where y is the estimated value of the dependent variable for the obser-vation i, b0 the intercept, bk the estimated parameter for the variable k,xik the value of the variable kth for i, and ei the error term(Fotheringham and Charlton, 1998).

The OLS approach calibrates a unique regression equation for all ofthe observations, while the GWR constructs a regression equation sep-arately for each observation, where each equation is calibrated using adifferent weighting of the observations in the dataset. The GWR model,represented by equation (2), allowed us to work with local parametersinstead of global parameters, i.e:

(eq. 2)

where ui and vi indicate the point coordinates of ith in space(Fotheringham et al., 2002). Regarding the assignment of the weight ofthe GWR model, a weighting scheme known as the adaptive Kernelmethod (with spatial variation) was used, which assigns larger densityvariation measures where the weighting points are disperse and minorones where they are more concentrated (Rojas et al., 2013).

The differences in the use of a global statistic model and a local one

such as the GWR are based mainly in the capacity of the latter to be spa-tialised and represented in a GIS environment with emphasis on thedifferences regarding space, local disaggregation of the local statistics,among others (Fotheringham et al., 2002). Although the GWR modelcan be advantageous in order to distinguish heterogeneity of the spaceitself and it also makes it easier to go from a global perspective to alocal analysis, thus obtaining a better grade of details and precision(Lloyd and Shuttleworth, 2005), it can also present reliability conflicts(Páez et al., 2011).

The calculations of the regression models (OLS and GWR) wereimplemented using the ArcGIS Modelling Spatial Relationships toolset.Multiple models were made using a set of candidate variables untilselecting a model with high explanatory power and that incorporatedthe six explanatory variables that are relevant from the point of view ofaccessibility to healthcare.

Results

Public hospital accessibilityFigure 3 shows the geographic distribution pattern of the accessibil-

ity values that follow the typical centre-periphery model in which thecity areas where hospital units are located show, most of the time, highlevels of accessibility (0.9 to 24.2 minutes). Furthermore, surroundingareas record intermediate levels of accessibility (24.2 to 33.1 minutes),and areas located far from health care centres (in southern CMA)showed unfavourable, or very unfavourable, accessibility levels with anaverage of higher than 30 minutes (33.1 to 104.8 minutes). Most ofthese were rural areas. It is important to emphasise the optimal levelsof access observed in the urban area of Concepción, Talcahuano,Hualpén, San Pedro de la Paz, and Penco (central conurbation), wheremost of the hospitals of the study area are concentrated (Regional

Article

Figure 2. Hospital assignment matrix per locality. 1) Regionalhospital; 2) Higueras hospital; 3) Penco-Lirquén hospital; 4)Tomé hospital; 5) Coronel hospital; 6) Lota hospital; 7) SantaJuana hospital.


Non co

mmercial

use o

nly

Hospital, Penco Hospital and Higueras Hospital). These areas alsoshowed good urban connectivity from the point of view of the networktopology. In this concentric area, average travel times to access hospitalunits ranged from 0.9 to 14.8 minutes.

In general, the variation in accessibility levels in CMA correspondsto the ease in arriving to a hospital, considering the network morphol-ogy as a useful aspect to identify infrastructure problems and, at thesame time, the low speeds determined by the topology of the road. Inthese areas, as in the case of the localities belonging to Hualqui andSanta Juana, the predominant type of road is rural, which in somecases do not allow motorised transport. Therefore, in these cases, peo-ple have no alternative to walking.

Ordinary least squaresThe OLS model summary (Table 4) shows that for a degree of confi-

dence of 95%, three out of the six explanatory variables are significant(P value), corresponding to connectivity, homes with a vehicle, andalternative housing. All of these present the expected coefficients. Thethree variables that are not significant in the global model are likewiseconsidered for the local model (GWR), with the aim of spatially evalu-ating the significance of their coefficients. Moreover, the varianceinflation factor (VIF) values (all below the threshold of 7.5) indicatethat there are no problems of multicollinearity among the explanatoryvariables.

Regarding the diagnostic model (Table 5), the global model fit (OLS)offers an adjusted R2 0.67, meaning that the variability in the traveltimes to hospitals can be explained with a precision of more than 60%with the six variables selected. The Jarque-Bera statistic (Jarque andBera, 1987) implies a significant P value, demonstrating that theregression residuals do not present a theoretical normal distribution.The Koenker statistic (BP) (Koenker, 1981) presents a statistically sig-nificant P value, indicating that the relationship between explanatoryand dependent variables is non-stationary (different in distinct spatialzones of the study area).

The decision to resort to spatial regression is justified when animprovement in the global fit is produced or when the presence of clus-ters is detected in the residual distribution that needs to be corrected(Gutiérrez et al., 2012). Considering these aspects, sufficient evidenceexists to turn to GWR.

Geographically weighted regression The adjusted R2 in the GWR model was found to be 0.87, a very impor-

tant improvement with respect to the figure (0.67) delivered by the OLSmodel. In addition, the Akaike information criterion value (Hurvich etal., 1998) is lower in GWR than OLS (845 and 941, respectively), andthis parameter indicates a better performance for the local model.

Article


Figure 3. Accessibility to public hospitals in Concepción metro-politan area.

Table 4. Ordinary least squares model summary.

Variable Coefficient SE P* VIF°

Intercept 60.183862 4.389099 0.000000 -Public transport routes -0.067006 0.053620 0.084646 2.113207Connectivity -28.414235 3.535520 0.000000 2.515939Homes with a vehicle -8.530927 3.765749 0.000179 1.218714Rural housing 43.943766 29.263301 0.321395 1.574576Alternative housing 85.806702 30.530654 0.044428 1.679720Illiterate population 26.089914 15.744198 0.060757 1.560206SE, standard error; VIF, variance inflation factor. *P<0.05; °indicator of redundancy between the explanatory variables (when their values surpass the threshold of 7.5).

Table 5. Ordinary least squares diagnostic model.

Statistics Diagnostic P

Adjusted R2° 0.677032 -AIC# 941.729 -Jarque-Bera statistic§ 135.512 0.000000BP statistic^ 27.2450 0.000301AIC, Akaike information criterion; BP, Koenker. °Coefficient indicating the relative goodness of fit of theregression; #measure of the model value of adaption – the lower the value, the higher the model’s per-formance; §approach to establish if the residuals of a regression model are normally distributed;^approach testing the spatial variability of the variables.


Non co

mmercial

use o

nly


Moreover, the residual analysis also shows better results in GWR thanin OLS. As shown in Table 6, this improvement can be statistically ver-ified. The calculated value of Moran’s I for the residuals is much closerto the expected index in the GWR model by showing a lower varianceand higher probabilities of random distribution (P values and Zscores).

Moreover, the spatial distribution of the local adjustments producedwith the GWR (local R2) provided information regarding the spatialvariation of the model’s explanatory power. The distribution of the localR2 at the district level varied between 0.60 and 0.80 (Figure 4), demon-strating that the model has a better explanatory capacity in the centralzone of CMA (districts belonging to municipalities of Concepción,Hualpén and Talcahuano), increasing the R2 above 0.73.

This trend shows that the adjustment decreases in zones wherethere is a lower density of districts (southern CMA), so these zoneshave a lower number of neighbours. On the other hand, zones withhigher density have more neighbours when adjusting the model (cen-tral zone), increasing the R2 above 0.71. For the spatial variabilityanalysis of the local coefficients of the explanatory variables (elastici-ty) in the GWR model, the spatial representation is shown from Figure5 to 10 together with statistically significant T values (measures thedifference between an observed sample statistic and its hypothesisedpopulation parameter in units of standard error) at the 90% level, withT values higher than 1.64 and not significant in some census districts.

The variable regarding the public transport routes (Figure 5) showedsignificant values in southern CMA, including the municipalities ofSanta Juana, Hualqui, Lota Coronel, part of San Pedro de la Paz,Chiguayante, and the rural area of Concepción, with high coefficientsin the districts belonging to the municipality of Santa Juana (-0.48 and-0.36), indicating a higher incidence of this variable in travel times.

Furthermore, the coefficients related to the variable of connectivity(Figure 6) are statistically significant in most of CMA, with the excep-tion of the Península de Tumbes (Talcahuano), where the structuralcomplexity of the road network does not significantly influence thetravel times to hospitals. The relationship between the variable of con-nectivity and the travel times was found to be negative in all areas stud-ied. The mean of the coefficients of this variable was -13.07, butreached very high values in the South (Hualqui-Santa Juana) and inthe North (Tomé) (-39.05 and -26.11, respectively) showing that traveltime to the hospitals has an important effect.

The variable homes with a vehicle (Figure 7) showed a negative rela-tionship with respect to the dependent variable. The highest coeffi-cients varied between -15.4 and -4.8. In this way, the highest/lowestnumber of homes with their own vehicle, in these zones, indicate adecrease/increase in travel time to hospitals. The coefficients that arestatistically significant are present in the districts belonging to themunicipalities of Tomé (northern CMA), in the rural areas ofConcepción, Chiguayante, and San Pedro de la Paz (central zone), andin Hualqui, Coronel, and Lota (in the South). The districts belonging toSanta Juana (in the South) and the central conurbation of the territorydid not provide evidence of statistically significant coefficients.

The variable related to rural housing (Figure 8) showed significantvalues in southern CMA, in the census districts belonging to themunicipalities of Santa Juana, Lota, Coronel, Hualqui and CMA’s cen-tral zone, specifically the municipalities of Talcahuano, Hualpén, andPenco. The highest coefficient values were observed in this area witha positive relationship influencing hospital travel times. In the districtsin the eastern part of CMA where there was a change in the sign (neg-ative relationship with respect to the dependent variable), the coeffi-cients were not statistically significant (with the exception of five cen-sus districts belonging to Hualqui). Almost all of Concepción and Tomé

presented statistically non-significant values.With respect to alternative housing (Figure 9), statistically signifi-

cant values were found in southern CMA (districts belonging toHualqui, Concepción, Coronel, Lota, and Santa Juana) with especiallyhigh coefficients seen in the municipalities of Santa Juana andHualqui (569.2-200.3, respectively). The coefficients indicate a positiverelationship with the dependent variable in the districts where it wassignificant, showing that the presence of alternative housing in thesezones is correlated with an increase in hospital travel times.

Finally, the illiterate population (Figure 10) showed its highest coef-ficients in southern CMA, i.e. the districts belonging to Santa Juanaand Hualqui (98.7-288.3, respectively), where they are statistically sig-nificant. The same was also the case in the the census districts of Lotaand other districts belonging to Coronel, Chiguayante, and Concepción.In these zones, the variable had a positive relationship with travel timeto hospitals.

Article

Table 6. Moran’s I in the residuals ordinary least squares and geo-graphically weighted regression.

Score OLS GWR

Moran’s I 0.251 0.019Expected index -0.008 -0.008Variance 0.001 0.000Z score 6.372 0.933P value 0.000 0.350Pattern Clustered RandomOLS, ordinary least squares; GWR, geographically weighted regression.

Figure 4. Spatial distribution of local R2 in the geographicallyweighted regression model.


Non co

mmercial

use o

nly

Article


Figure 6. Connectivity: spatial distribution of the local coefficients and T values in the geographically weighted regression model.

Figure 5. Public transport routes: spatial distribution of the local coefficients and T values in the geographically weighted regressionmodel.


Non co

mmercial

use o

nly


Article

Figure 8. Rural housing: spatial distribution of the local coefficients and T values in the geographically weighted regression model.

Figure 7. Homes with a vehicle: spatial distribution of the local coefficients and T values in the geographically weighted regressionmodel.


Non co

mmercial

use o

nly

Article


Figure 10. Illiterate population: spatial distribution of the local coefficients and T values in the geographically weighted regressionmodel.

Figure 9. Alternative housing: spatial distribution of the local coefficients and T values in the geographically weighted regression model.


Non co

mmercial

use o

nly


Discussion

This research found that approximately 4.1% of the population(37,228 people) living in the CMA (900,000 people) have unfavourableor very unfavourable access to public hospitals (travel times above 30and 45 minutes, respectively). Of this population, 32.8% live in ruralareas, especially in the municipalities of Tomé, Santa Juana, andHualqui, where areas of particular low accessibility to hospitals wereidentified. In these locations, population has a strong need to increaseits hospital accessibility, which is primarily due to long travel times.

The modelling of hospital accessibility using socio-economic andtransportation variables elucidated local variations of the explanatoryvariables under study, some of which were found to have a strong influ-ence on the hospital travel times in southern CMA. The relationshipamong the census variables of population, homes, and housing and thedependent variable suggests that, in general, the zones with shortertravel times to the hospital network centres showed better socio-eco-nomic characteristics when compared to those with longer ones. Thisaspect is in line with the results found by Bagheri et al. (2009) in theexploration of the local variation of the accessibility to primary healthcare based on a deprivation index in an GWR analysis. Likewise, Shahand Bell (2013) have published reports, where the advantages of thismethod are shown in the disaggregation of the relationships betweensocio demographic variables and the geographic accessibility to the pri-mary health care services at the local scale.

The OLS model, on the other hand, showed that three out of the sixvariables were statistically significant. However, the results of the glob-al regression are only averages of the total studied region and couldconceal a large amount of interesting spatial variation in the relation-ships appearing in the local analysis (Bagheri et al., 2009). Thisbecomes a problem when trying to understand how the relationshipsamong variables change throughout the space investigated. Regardingthis, the GWR model generates a local adjustment in multiple locations,repeating the process for all variables.

Regarding model performance, the OLS gives an adjusted R2 of 0.67,while the GWR shows an adjusted R2 of 0.87. Considering the six select-ed variables in this study, the variability of the travel times to hospitalscan be explained with an accuracy of over 80%, implying an importantimprovement with respect to the OLS model. The results identified themost deprived zones regarding spatial access to hospitals, and they alsoshowed the highest coefficients of the selected variables.

As to the variables selected for this research, the socio-demographiccharacteristics based on the census used to analyse local healthinequalities, focusing on the determinant needs of health care servic-es, are increasingly used in health geography (Andersen et al., 2007;Chateau et al., 2012). For example, studies concerning social inequali-ties in healthcare have shown that for both sexes and all ages, the mostdeprived social classes have worse health indicators than the popula-tion belonging to more privileged social classes. The same has beenshown for the poorest people or geographic areas and people or geo-graphic zones with greater wealth (Benach and Amable, 2004). Theseaspects are clearly related to situations in our study areas in CMA.

It is important to note that one of the study limitations is that ourresearch addresses accessibility to healthcare as a linear component oftravel (relationship between an origin and a destination), and not fromthe perspective of the use and/or completion of health benefits.Therefore, the studies of mobility in health substitute this link to therelationship between a need (to receive attention in the public healthsystem) and its satisfaction (to specify health benefits); the firstapproach is insufficient for this type of research, especially in the study

of cases requiring prolonged medical treatment or periodic checks. Inthis sense, due to the marked inequality in Chile, further research isrequired from the perspective of geography and transportation.

Conclusions

Measuring the accessibility to health care establishments in a met-ropolitan area not only identifies areas of the territory with criticalproblems, but also strengthens the analysis regarding the inequality toaccessing healthcare, an aspect difficult to assess with the classic geo-graphic approach that uses accessibility to service or coverage byhealth care establishments with location as a single fundamental ele-ment. Modelling at the local scale shows many advantages over theglobal multiple regression model (Gutiérrez et al., 2012), as it providesinformation on areas of higher and lower adjustments, spatial relation-ship dynamics and their statistical significance. Indeed, we haveshown the importance of considering local analysis in studies relatedto accessibility to health care, which should be understood as a meansof overcoming the distance as an important instrument for determin-ing existing inequalities in a territory. The geographic accessibilitymodels have an enormous potential to contribute to policy developmentand to debate about the way to reach equality in accessibility to hospitalestablishments. Models are a critical resource that can be used by plan-ners to give priority to the location and assignment of health services(Brabyn and Skelly, 2002). The application of geographic analysis pro-cedures focused on solving empirical problems in the field of healthgeography is shown nowadays as a research area of great dynamismsince its methodological procedures are supported by current GIS tech-nology (Buzai, 2009).

References

Andersen R, Davidson P, Baumeister S, 2007. Improving access to care.In: Kominski GF, ed. Changing the US health care system: keyissues in health services policy and management. pp 33-70. Wiley,Hoboken, NJ, USA.

Bagheri N, Holt A, Benwell G, 2009. Using geographically weightedregression to validate approaches for modelling accessibility to pri-mary health care. Appl Spat Anal Policy 2:177-94.

Benach J, Amable M, 2004. [Las clases sociales y la pobreza]. [Articlein Spanish]. Gac Sanit 18:16-23.

Bocco G, Mendoza M, Masera O, 2000. [La dinámica del cambio del usodel suelo en Michoacán. Una propuesta metodológica para el estu-dio de los procesos de deforestación]. [Document in Spanish].Invest Geog 44:18-38.

Bollen KA, Barb KH, 1981. Pearson’s r and coarsely categorized meas-ures. Am Sociological Review 46:232-9.

Brabyn L, Skelly C, 2001. Geographical access to services, health (GASH):modelling population access to New Zealand public hospitals.Available from: www.geocomputation.org/2001/papers/brabyn. pdf

Brabyn L, Skelly C, 2002. Modeling population access to New Zealandpublic hospitals. Int J Health Geogr 1:3.

Buzai GD, 2009. [Sistemas de información geográfica en geografía dela salud]. In: Buzai GD, ed. [Salud y enfermedad en geografía].[Book in Spanish]. Lugar Editorial, Buenos Aires, Argentina, pp111-34.

Buzai GD, 2011. [Modelos de localización-asignación aplicados a servi-

Article


Non co

mmercial

use o

nly

cios públicos urbanos: análisis espacial de Centros de AtenciónPrimaria de Salud (CAPS) en la ciudad de Luján, Argentina].[Article in Spanish]. Cuad Geogr 20:111-23.

Chateau D, Metge C, Prior H, Soodeen R, 2012. Learning from the cen-sus: the socio-economic factor index (SEFI) and health outcomesin Manitoba. Can J Public Health 8:23-7.

Dewulf B, Neutens T, De Weerdt Y, Van De Weghe N, 2013. Accessibilityto primary health care in Belgium: an evaluation of policies award-ing financial assistance in shortage areas. BMC Fam Pract 14:122.

Fotheringham AS, Brunsdon C, Charlton M, 2002. Geographicallyweighted regression: the analysis of spatially varying relationships.Wiley, Hoboken, NJ, USA.

Fotheringham AS, Charlton M, 1998. Geographically weighted regres-sion: a natural evolution of the expansion method for spatial dataanalysis. Environ Plann A 30:1905-27.

Fuenzalida M, 2010. [Análisis de desigualdades territoriales en la ofer-ta de equipamientos públicos: el caso de los hospitales en la redasistencial del sistema público de salud en Chile]. [Article inSpanish]. Geografía y Sistemas de Información Geográfica 2:111-25.

Fuenzalida M, Guerrero R, Cobs V, 2014. [El uso de la técnica de auto-correlación espacial en la definición de los determinantes socialesde la salud del Área Metropolitana de Santiago de Chile]. [Articlein Spanish]. In: Proceedings of the 16th National Congress ofTechnologies of Geographic Information, Alicante, Spain. Availablefrom: rua.ua.es/dspace/bitstream/10045/46507/1/2014_Fuenzalida_etal_Congreso_TIG.pdf

Gutiérrez J, García Palomares JC, Cardozo O, 2012. [RegresiónGeográficamente Ponderada (GWR) y estimación de la demanda delas estaciones del Metro de Madrid]. [Article in Spanish]. In:Proceedings of the 15th National Congress of Technologies ofGeographic Information, Madrid, Spain.

Hare T, Barcus H, 2007. Geographical accessibility and Kentucky’sheart-related hospital services. Appl Geogr 27:181-205.

Hurvich CM, Simonoff JS, Tsai C-L, 1998. Smoothing parameter selec-tion in nonparametric regression using an improved Akaike infor-mation criterion. J Roy Stat Soc B 60:271-93.

INE, 2002. Population and Housing Census of Chile. Latin AmericanCenter of Demography (CELADE). National Statistical Institute ofChile, Santiago de Chile, Chile. Available from:http://espino.ine.cl/cgibin/RpWebEngine.exe/PortalAction?&MODE=MAIN&BASE=CPCHL2KREG&MAIN=WebServerMain.inl

Jarque C, Bera A, 1987. A test for normality of observations and regres-sion residuals. Int Stat Rev 163-72.

Koenker R, 1981. A note on studentizing a test for heteroscedasticity. JEconometrics 17:107-12.

Lloyd CD, Shuttleworth I, 2005. Analysing commuting using local

regression techniques: scale, sensitivity, and geographical pattern-ing. Environ Plann A 37:81-103.

Munoz U, Kallestal C, 2012. Geographical accessibility and spatial cov-erage modeling of the primary health care network in the WesternProvince of Rwanda. Int J Health Geogr 11:40.

Páez A, Farber S, Wheeler D, 2011. A simulation-based study of geo-graphically weigthed regression as a method for investigating spa-tially varying relationships. Environ Plann A 43:2992-3010.

Páez A, Mercado RG, Farber S, Morency C, Roorda M, 2010. Accessibilityto health care facilities in Montreal Island: an application of rela-tive accessibility indicators from the perspective of senior and non-senior residents. Int J Health Geogr 9:52.

Patel A, Waters N, 2012. Using geographic information systems forhealth research. In: Alam BM, ed. The geographic informationsystem. In-Tech, Rijeka, Croatia, pp 303-20.

Ramírez M, Bosque Sendra J, 2001. [Localización de hospitales: analo-gías y diferencias del uso del modelo P-mediano en Sig raster y vec-torial]. [Article in Spanish]. Ann Geogr Univ Complut 21:53.

Rodríguez V, 2010. [Medición de la accesibilidad geográfica de la pobla-ción a la red de hospitales de alta resolución de Andalucía median-te sistemas de información geográfica]. In: Díaz-Delgado R,Pesquer L, Prat E, Bustamante J, Masó J, Pons J, eds. [Tecnologíasde la información geográfica: la información geográfica al serviciode los ciudadanos]. [Book in Spanish]. University of Seville,Seville, Spain, pp 549-64.

Rojas C, Plata W, Valdebenito P, Muñiz I, De la Fuente H, 2013. [La diná-mica de expansión urbana del area metropolitana de Concepción].In: Williams J, Hidalgo R, Brand P, Pérez L, eds. [MetropolizacionesColombia-Chile: experiencias de Bogotá, Medellín, Santiago yConcepción]. [Book in Spanish]. National University of Colombia,Bogotá, Colombia, pp 39-56.

Sasaki S, Comber A, Suzuki H, Brunsdon C, 2010. Using genetic algo-rithms to optimise current and future health planning-the exampleof ambulance locations. Int J Health Geogr 9:4.

Schuurman N, Fiedler R, Grzybowski S, Grund D, 2006. Defining ration-al hospital catchments for non-urban areas based on travel-time.Int J Health Geogr 5:43.

Shah TI, Bell S, 2013. Exploring the intra-urban variations in the rela-tionship among geographic accessibility to PHC services and socio-demographic factors. Proceedings of the Second ACM SIGSPATIALInternational Workshop on the Use of GIS in Public Health, 2013November 05-08, Orlando, FL, USA, pp 68-76.

Villanueba A, 2010. [Accesibilidad geográfica a los sistemas de salud yeducación. Análisis espacial de las localidades de Necochea yQuequén]. [Article in Spanish]. Revista Transporte y Territorio2:136-57.

Article



Non co

mmercial

use o

nly

Documents

Geographically weighted regression for modelling the